I have run that particular diode off of two li-ion batteries without a driver and it didn't die, if it either gets too hot or is driven too hard the output will get lower and lower and recover after the voltage is removed and put back on. This however is abusing the diode and will likely result in reduced life. That said, you could just hook up the nominal voltage the manufacturer specifications call for to test it without a constant current driver, as long as it is heat sinked, if only for a moment, and I wouldn't be afraid of destroying it, given I've run more than one of these for long periods of time without a driver and no failure yet.... Still, it is abusing the diode.
Of course, if you try it, the diode will fail the first try, that's how these things usually go.